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This paper presents a systematic approach for the design and optimization of a dual-antenna structure for RFID tags. In order to successfully design a dual-antenna structure, the input impedance of the receiving antenna should be conjugate matched to that of the tag chip, and the input impedance of the backscattering antenna must be purely real. To achieve the design goals for both antennas while keeping a low mutual coupling, the design of experiments (DOE) technique is adopted, and the regression models in terms of geometric parameters can be attained via the analysis of variance (ANOVA). With these models, the response variables can be predicted. A series of solutions toward these models can be obtained by formulating the problem into a constrained optimization problem; these solutions are further ranked according to their Derringer's desirability function. The solution with the higher overall desirability are whereby considered as the optimal design. with this systematic approach, the design procedure is greatly simplified.